On the Intertemporal Risk-Return Relation: A Bayesian Model Comparison Perspective - Wang, Leping (Institutional Knowledge at Singapore Management University, 2005)
The existing empirical studies indicate that inferences on the intertemporal relation between expected return and volatility are highly sensitive to empirical specifications of return dynamics. Glosten, Jagannathan, and Runkle (1993) attempt to resolve this confusing situation by examining several generalizations of the standard GARCH-M model. They conclude a negative risk-return relation solely based on the models that are identified in the first step through a variety of diagnostic tests as relatively “better” models. However, it has not been shown in their study whether the evidence supporting their first-step model selection decision is significant or not. To the extent the strength of sample evidences supporting those selected models is unclear, it remains unconvincing whether their finding of a negative risk-return relation is significant or not. Accordingly, our paper propose a Bayesian model comparison approach to explicitly assess the strength of the evidence in support of the models that typically indicate conflicting signs for the risk-return relation. The empirically computed Bayes factors show that the models that indicate a negative risk-return relation indeed outperform, at a decisive degree, the alternative models that suggest a contrary result. Further, with priors that slightly favor return nonpredictability, evidence still indicates a negative relation after model uncertainty is accounted for. Therefore, our study complements the work of Glosten, Jagannathan, and Runkle (1993) by showing that not only the parameter relating risk to return is estimated to negative and significant for the selected model, but also the selected model is favored by the data at a significant degree.